Mr Trump hopes Mr Pence - a former congressman popular among social conservatives - can help him shore up support among wavering Republicans.

"My family and I couldn't be more honoured to have the opportunity to run with and serve with the next president of the United States," Mr Pence told reporters in New York on Friday.

Other candidates in the running were former House Speaker Newt Gingrich and New Jersey Governor Chris Christie.

Analysis: Anthony Zurcher, BBC News, North America reporter

Image copyrightReutersImage caption
The two appeared in Indiana together this week

If there's anything resembling a "safe" vice-presidential pick for Donald Trump, Mike Pence is it. He has executive experience as Indiana's governor and a strong legislative resume from his 12 years as a member of the US House of Representatives.

While in Washington, he chaired the Republican Study Group, a coalition of hard-core conservatives, which gives him solid bona fides among the grass-roots Tea Party wing of the party that has occasional doubts about Mr Trump's ideological purity.

Mr Pence also hails from the mid-west, which Mr Trump's team has identified as perhaps the key battleground in his quest for the White House.

In Republican circles Mr Pence's record isn't entirely clean, however. Some on the right have criticised the governor for backing down when the state's "religious liberty" law was challenged by LGBT activists and local businesses last year.

Mr Pence's decision to expand government health-care coverage for Indiana's poor is also considered ideological heresy by some.

The real question, however, is whether Mr Pence has the rhetorical dexterity to both fulfil the traditional running-mate role of political attack dog on the stump and the nominee's most ardent defender.